That is an interesting idea for a story! If it's written well it could turn into a really good read!

Your idea makes sense (no disease = high population). If it were to actually happen, I think China would be either the first country to start conquesting for more territory or the first to collapse (as their population right now is pretty high). After that, the countries with the most space would become the super powers.

I think abit more on this next time I get baked, maybe I can come up with some more stuff :P

Good luck writing!